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1 
Koliha–Drazin invertibles form a regularitySmit, Joukje Anneke 10 1900 (has links)
The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms
are satisfied. However, there arise a number of spectra, usually defined for a single element
of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and
V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was
to describe the underlying set of elements on which the spectrum is defined. The axioms of a
regularity provide important consequences. We prove that the set of KolihaDrazin invertible
elements, which includes the Drazin invertible elements, forms a regularity. The properties of
the spectrum corresponding to a regularity are also investigated. / Mathematical Sciences / M. Sc. (Mathematics)

2 
Koliha–Drazin invertibles form a regularitySmit, Joukje Anneke 10 1900 (has links)
The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms
are satisfied. However, there arise a number of spectra, usually defined for a single element
of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and
V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was
to describe the underlying set of elements on which the spectrum is defined. The axioms of a
regularity provide important consequences. We prove that the set of KolihaDrazin invertible
elements, which includes the Drazin invertible elements, forms a regularity. The properties of
the spectrum corresponding to a regularity are also investigated. / Mathematical Sciences / M. Sc. (Mathematics)

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